Question

Which of the following is equal to the fraction below? (7/4)^ 11

Answer 1

When you multiply an exponent directly into another exponent, you multiply the exponents

(for a fraction, you multiply the exponent to both the numerator and denominator)

For example:

`(x^(2))^5=x^(2(5))=x^(10)`

`((x^3)/(y^2) )^5=(x^(3(5)))/(y^(2(5))) =(x^(15))/(y^(10))`

`((7)/(4))^(11)=((7^1)/(4^1))^(11)=(7^(11))/(4^(11))`

Your answer is A

Answer 2

`((7^(11))/(4^(11)))`

Explanation:

`((7)/(4))^(11)`

To simplify this fractional exponent we apply exponential property

`((x)/(y))^m=(x^m)/(y^m)`

As per this property , we multiply the exponent inside the fraction

Multiply the exponent 11 inside the fraction

Multiply the exponent 11 with 7 and then 4

`((7)/(4))^(11)`

`((7^(11))/(4^(11)))`